A Comparison of West Virginia’s 21st Century Reading and
English Language Arts Content Standards and Objectives, the
21st Century Mathematics Content Standards and Objectives,
and the 21st Century Learning Skills and Technology Tools
Content Standards and Objectives, with the American
Diploma Project Benchmarks for College and Career
Readiness
A Report submitted by Achieve to the West Virginia Department of
Education on January 15, 2009
TABLE OF CONTENTS
Introduction ..................................................................................................................................... 3
Major Findings & Recommendations: English Language Arts ...................................................... 6
Major Findings & Recommendations: Mathematics .................................................................... 20
Appendix A: Biographies ............................................................................................................. 32
Appendix B: Side-by-Side Chart for English Language Arts ....................... see attached document
Appendix C: Side by Side Chart for Mathematics........................................ see attached document
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January 15, 2009
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INTRODUCTION
Achieve is a bipartisan, non-profit organization created by the nation’s governors and corporate
leaders to help states raise their academic standards, improve their assessments, and strengthen
accountability to prepare all young people for postsecondary education, work, and citizenship. A
principal part of Achieve’s mission is to provide state policymakers with an independent, expert
review of the quality of their standards and tests. Achieve has been conducting reviews of
standards for 10 years, by benchmarking a state’s Academic Standards to exemplary standards.
For the purposes of this review, West Virginia standards in English, mathematics, learning skills
and technology tools are compared to the American Diploma Project (ADP) Benchmarks which
are the result of two years of research with employers and faculty from two- and four-year
colleges regarding what knowledge and skills are critical for success after high school.
The Development of the American Diploma Project (ADP) Benchmarks and Identification of
the ADP Core
The American Diploma Project commissioned leading economists to examine labor market
projections for the most promising jobs—those that pay enough to support a small family and
provide real potential for career advancement—to pinpoint the academic knowledge and skills
required for success in those occupations. ADP then surveyed officials from 22 occupations,
ranging from manufacturing to financial services, about the skills they believe are most useful
for their employees to bring to the job. Following those conversations, ADP worked closely
with two- and four-year postsecondary leaders in the partner states to determine the prerequisite
English and mathematics knowledge and skills required for success in entry-level, credit-bearing
courses in English, mathematics, the sciences, and the humanities. The resulting ADP
Benchmarks reflect an unprecedented convergence in what these employers and postsecondary
faculty say are needed for new employees and freshmen entering credit-bearing coursework to be
successful.
During this original ADP research, college faculty and employers highlighted two categories of
critical shortcomings in the preparation of many recent high school graduates. The first was
deficiency in the specific and narrow foundational skills typically taught in middle school. The
other was a lack of complex and conceptual competencies acquired late in high school that take
students several years to develop. While helping states align their standards to college- and
career-ready expectations, Achieve has heard these same concerns echoed across the country.
Based on these insights and Achieve’s extensive experience evaluating state standards, Achieve
content experts have identified within the ADP Benchmarks a core set of essential
understandings that states must include in their standards if they are to address these critical gaps
and ensure that their graduates are well prepared for college and careers. Although a well
prepared high school graduate will have mastered all of the knowledge and skills found in the
ADP Benchmarks, the “ADP Core” contained within the Benchmarks represents a vital subset of
college- and career-ready expectations, and these Common Core Benchmarks are noted as such
in both the mathematics and English language arts side-by-side charts provided with this report.
Achieve Report
January 15, 2009
page 3
Methodology
The state of West Virginia requested Achieve to compare the state’s 21st Century Reading and
English Language Arts Content Standards and Objectives (ELACS&O) and 21st Century
Mathematics Content Standards and Objectives (MCS&O), as well as the 21st Century Learning
Skills and Technology Tools Content Standards and Objectives (LSTCS&O), with the ADP
Benchmarks for College and Career Readiness.
Achieve’s analysis describes the extent to which the West Virginia Content Standards and
Objectives in English language arts, mathematics, and technology include the content important
for success in college and careers, as represented by the ADP Benchmarks. In this report,
Achieve set out to determine whether the CS&O represent a level of rigor that is characteristic of
the ADP Benchmarks.
In addition to this report, Achieve has created side-by-side charts (Appendices B and C) that
compare the West Virginia ELACS&O and the LSTCS&O with the ADP English Benchmarks
and another side-by-side chart that compares the West Virginia CS&O in mathematics with the
ADP Mathematics Benchmarks. The Learning Skills and Technology Tools are included in the
side-by-side chart for English language arts, and any relevant LS&TCS&O are also included in
the mathematics side-by-side chart. The ADP Benchmarks that represent a common core - a
vital subset of college- and career-ready expectations that have emerged from the alignment
process in 12 states in English and 16 states in mathematics are noted [ADP Core].1
In the side-by-side chart included with this report, the degree of alignment between an ADP
Benchmark and one or more West Virginia objectives judged to align with that benchmark is
evaluated. A numerical score ranging from “0” to “3” is assigned to each match to define the
degree of alignment. In mathematics, an asterisk (*) or a numerical rating accompanied by an
asterisk is noted in the Rating column. This signifies, as described in greater detail below, that
all or part of a state standard exceeds the expectations in ADP Benchmarks. These ratings can be
interpreted as follows:
3 = excellent alignment between the two documents
2 = good alignment, with minor aspects of an ADP Benchmark not addressed
1 = weak alignment, with major aspects of an ADP Benchmark not addressed
0 = no match for an ADP Benchmark was found
* = content expectations exceed those in the ADP Benchmarks [this rating may be used alone
(*) or with a 2- or 3-rating (2* or 3*)—e.g., in the case of a 2* or 3* rating, part of the state’s
standard aligns with the ADP counterpart, but there are parts of the standard that exceed the
ADP Benchmark requirement.]
As needed, commentary is provided in the last column of the side-by-side chart to clarify the
reasoning that went into assignment of the numerical rating.
West Virginia Materials Reviewed
1
Out of Many, One: Toward Rigorous Common Core Standards from the Ground Up, Achieve, July
2008 , available online at http://www.achieve.org/node/1019.
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January 15, 2009
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Achieve content experts evaluated the 21st Century Reading and English Language Arts Content
Standards and Objectives for West Virginia Schools (Policy 2520.1) – Grades 9, 10, 11 & 12;
the 21st Century Mathematics Content Standards and Objectives for West Virginia Schools
(Policy 2520.2) – Algebra I, Geometry & Algebra II & Trigonometry; and the 21st Century
Learning Skills and Technology Tools Content Standards and Objectives for West Virginia
Schools (Policy 2520.14) – Grades 9-12.
West Virginia high school standards are organized around the three major components of a
standards-based curriculum: learning standards, instructional objectives, and performance
descriptors. The learning standards are the broad descriptions of what all students must know
and be able to do at the conclusion of the instructional sequence. The accompanying grade-level
objectives are specific descriptors of knowledge, skills, and attitudes that when mastered will
enable the student to attain the standard. They are incremental steps toward accomplishment of
content standards, are listed by grade level, and are organized around the content standards.
Objectives build across grade levels as students advance in their knowledge and skills. They
guide instructional planning and provide a basis for determining appropriate assessments,
instructional strategies, and resources. The content standards and objectives provide a focus for
teachers to teach and students to learn and were evaluated as to what extent they align to the
ADP Benchmarks.
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January 15, 2009
page 5
MAJOR FINDINGS & RECOMMENDATIONS:
ENGLISH LANGUAGE ARTS
Overview
For purposes of this analysis, Achieve staff constructed a side-by-side chart comparing
Achieve’s American Diploma Project (ADP) English Benchmarks with the 21st Century
Reading and English Language Arts Content Standards and Objectives for West Virginia
Schools (21st Century ELA Standards) and the 21st Century Learning Skills and Technology
Tools Content Standards and Objectives for West Virginia Schools (21st Century Learning and
Technology Standards). The Achieve study focused on Grades 9-12. However, since the ADP
Benchmarks are cumulative in nature, in some instances objectives from lower grades were used
to complete the chart. Commentary can be found in both this summary report and in the fifth
comment column of the side-by-side chart.
West Virginia’s 21st Century Reading and English Language Arts Content Standards and
Objectives are constructed in three strands: reading, writing, and listening/speaking/media, with
separate levels for each of the high school grades as well as for a speech course and for a
journalism course. The format consists of learning standards that are broad descriptions of what
all students must know and be able to do at the conclusion of the instructional sequence, grade
level objectives that are specific descriptors that guide instruction and assessment for that grade,
and performance descriptors that define five levels of student performance ranging from novice
to distinguished.
The state’s 21st Century Learning Skills and Technology Tools Content Standards and
Objectives are described for grade bands: PreK-2, Grades 3-4, 5-8, and 9-12. The West Virginia
Standards for 21st Century Learning integrate 21st century learning skills and 21st century
technology tools into three standards:
Standard 1: Information and Communication Skills
Standard 2: Thinking and Reasoning Skills
Standard 3: Personal and Workplace Skills
Each standard is followed by relevant Learning Skills Objectives and Technology Tools
Objectives. The grade band 9-12 objectives included in this set of standards were included in the
comparison of the state’s expectations to the ADP Benchmarks.
The side-by-side chart found in Appendix B includes the state’s grade level objectives for
English language arts in Grades 9-12.
Alignment Analysis
Overall, the alignment between the West Virginia standards and the ADP English Benchmarks is
good. Much of the content of ADP is represented within either West Virginia’s 21st Century
English Language Arts Standards, or in its 21st Century Learning and Technology Standards, or
Achieve Report
January 15, 2009
page 6
in both sets of expectations. West Virginia joins 12 states that have completed the
alignment process and emerged with a similar Common Core of college- and careerready standards that align with a critical subset of the ADP English Benchmarks.2
The selected West Virginia 21st Century Content and Technology Standards define rigorous
expectations that generally align well with the ADP Benchmarks with some exceptions. What
follows is a description of some general commonalities and differences found between the two
sets of standards.
Finding 1: While the overall alignment is good between the West Virginia standards
and the ADP English Benchmarks, in some instances the ADP Benchmarks do not have
a counterpart in the West Virginia standards. The logic strand is an area of particular
concern.
The ADP Benchmarks in English are organized into eight strands:
A.
B.
C.
D.
E.
F.
G.
H.
Language
Communication
Writing
Research
Logic
Informational Text
Media
Literature
When alignment with a set of state standards is considered, Achieve looks at the content of the
state standards against each of these eight strands of the ADP Benchmarks.
Across all eight strands, the alignment between the West Virginia expectations and ADP is good
when both the 21st Century English Language Arts Standards and the 21st Century Learning
and Technology Standards are considered. West Virginia includes statements on
workplace/functional writing and group work, areas often neglected in state English language
arts standards.
West Virginia does have some gaps, however, when compared with the content of ADP. These
gaps, as well as areas of weaker alignment that are discussed in the next section, are most notable
in the areas of Logic and Literature.
Of the 22 Common Core English benchmarks, the West Virginia standards meet 18 of
them, with the weakest alignment in the Logic strand. In Logic, one Common Core
benchmark (ADP E8) was not matched to a complimentary state standard, two Common
Core benchmarks (ADP E1 and E4) had very low ratings of "1,” and two other
benchmarks in this strand (ADP E2 and E6) were also absent from the state’s materials.
2
Out of Many, One: Toward Rigorous Common Core Standards from the Ground Up, Achieve, July
2008, page 7, Table 1: ADP Core in English. See http://www.achieve.org/node/1019.
Achieve Report
January 15, 2009
page 7
In general, logic proved to be the area most lacking in the West Virginia materials
reviewed. The state’s standards were also weak in their alignment to the ADP Literature strand,
chiefly since the state did not include U.S. documents as materials to study nor did they include
expectations on drama or attention to the moral dilemmas encountered in literature.
TABLE 1 below shows the ADP Benchmarks that have no counterparts in either the West
Virginia 21st Century English Language Arts Standards or 21st Century Learning and
Technology Standards. Ratings of “0” were assigned in the accompanying side-by-side chart
since there is no match for these Benchmarks.
TABLE 1 – ADP Benchmarks that are not addressed in the West 21st Century ELA
Standards and 21st Century Learning and Technology Standards
Research
D4. Report findings within prescribed time and/or length requirements, as appropriate.
Logic
E2. Identify false premises in an argument.
E6. Analyze written or oral communications for false assumptions, errors, loaded terms,
caricature, sarcasm, leading questions and faulty reasoning.
E8. (Common Core) Analyze two or more texts addressing the same topic to determine how
authors reach similar or different conclusions.
Informational Text
F4. Distinguish between a summary and a critique.
F10. Recognize the use or abuse of ambiguity, contradiction, paradox, irony, incongruities,
overstatement and understatement in text and explain their effect on the reader.
Literature
H2. Analyze foundational U.S. documents for their historical and literary significance (for
example, The Declaration of Independence, the Preamble to the U.S. Constitution, Abraham
Lincoln’s “Gettysburg Address,” Martin Luther King’s “Letter from Birmingham Jail”).
H6. Identify how elements of dramatic literature (for example, dramatic irony, soliloquy, stage
direction and dialogue) articulate a playwright’s vision.
H8. (Common Core) Analyze the moral dilemmas in works of literature, as revealed by
characters’ motivation and behavior.
Finding 2: In some instances, the alignment between the West Virginia standards and
the ADP English Benchmarks is not as complete or as clear and explicit as it could be.
In the attached side-by-side comparison chart, Achieve uses ratings of “1” or “2” to show those
instances in which the West Virginia standards do not address key elements of ADP (rating of
“2”) or are weakly matched with ADP (rating of “1”). Weak ratings and/or comments in the
chart indicate gaps in content or performance alignment, or what appear to be differences in the
level of expectation, given the wording used in the West Virginia standards.
For example, in the Communication strand, statements in the West Virginia standards are only
somewhat aligned with ADP B4—“Identify the thesis of a speech and determine the essential
elements that elaborate it.” While West Virginia does specify that students will “locate and
analyze … author’s … main and supporting details” (RLA.O.9.1.05), this expectation appears
Achieve Report
January 15, 2009
page 8
only in the Reading section of West Virginia, rather than in the Speech section. It may be
inferred from this that students are not expected to transfer this skill into situations in which
information is conveyed orally, rather than in writing.
In the Logic strand, ADP E1—“Distinguish among facts and opinions, evidence and
inferences”—is only partially met by West Virginia expectations. West Virginia does include
statement RLA.O.9.3.04, which states that students will “use active listening strategies to …
differentiate fact from opinion.” This statement, however, appears under only Listening,
Speaking, and Media Literacy. In addition, no statement on Reading appears to address
explicitly the expectation that students will analyze arguments and distinguish between evidence
that supports an argument and inferences that authors make to support their arguments.
Additional cases where the full expectation defined in an ADP Benchmark is not covered
completely or well by the West Virginia are indicated in TABLE 2 with a rating of “1” or “2.”
TABLE 2 – ADP Benchmarks that are not explicitly or completely addressed in the West
Virginia 21st Century ELA Standards and 21st Century Learning and Technology Standards
ADP
West Virginia
Rating
Comments
A5. Identify the
1
Idioms and allusions may be implied, but
RLA.O.10.1.05
meaning of common
neither is stated explicitly in the West
RLA.O.10.1.10
idioms, as well as
Virginia standards for English language
RLA.O.9.1.10
literary, classical and
arts in Grades 9-12. Both are important
biblical allusions...
for instruction—particularly for students
for whom English is a second language
or for students who may not have a rich
home experience with literature and
language, as home is often where
students with stronger literacy
environments would acquire this
knowledge of idioms and allusions.
A7. Comprehend and
1
The emphasis in West Virginia is on the
21C.O.9communicate
communication of technical information,
12.1.LS3
quantitative, technical 21C.O.9rather than on the comprehension.
and mathematical
Expectations for comprehending (and
12.1.TT6
information.
communicating) quantitative and
21C.O.9mathematical information may logically
(Common Core)
12.1.TT8
appear in West Virginia in the
mathematics and science objectives.
The West Virginia statements included
here go beyond the scope of ADP in the
specificity of expectations on using
spreadsheet and database software.
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January 15, 2009
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ADP
B4. Identify the thesis
of a speech and
determine the essential
elements that elaborate
it. (Common Core)
E1. Distinguish among
facts and opinions,
evidence and
inferences. (Common
Core)
E3. Describe the
structure of a given
argument; identify its
claims and evidence;
and evaluate
connections among
evidence, inferences
and claims.
E4. Evaluate the range
and quality of
evidence used to
support or oppose an
argument. (Common
Core)
E5. Recognize
common logical
fallacies, such as …
West Virginia
RLA.O.10.1.05
RLA.O.9.1.05
Rating
2
Comments
In West Virginia, these related statements
come from the Reading strand instead of
from the Listening, Speaking and Media
Literacy strand.
RLA.O.4.1.08
RLA.O.9.3.04
1
RLA.O.12.1.12
RLA.O.11.1.12
RLA.O.10.1.11
2
The analysis of arguments—including
distinguishing among evidence and
inferences—does not appear to be
addressed in the West Virginia
statements.
Emphasis in West Virginia statements
seems to be on persuasive language and
techniques rather than on the structure of
arguments, the strength of evidence, and
the relationships among evidence,
inferences, and claims.
21C.O.912.1.LS1
1
West Virginia does not appear to state
explicitly that it expects students to
evaluate the strength of evidence used to
support an argument.
RLA.O.12.1.12
RLA.O.11.1.12
RLA.O.10.1.11
1
E7. Understand the
distinction between a
deductive argument …
and inductive
argument …
RLA.O.12.1.12
2
G2. Examine the
intersections and
conflicts between the
visual (such as media
images, painting, film
and graphic arts) and
the verbal.
21C.O.912.1.LS2
1
West Virginia may want to consider
whether it wants to include the
expectation that students can understand
and analyze various logical fallacies.
West Virginia may want to make the type
/ structure of arguments a separate
statement, rather than grouping
persuasive language / techniques together
with type / structure, as these might apply
to different types of texts.
West Virginia does not explicitly address
intersection of visual and verbal—
although this statement in 21st century
standards does suggest that students can
analyze/interpret visual elements.
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January 15, 2009
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ADP
H1. Demonstrate
knowledge of 18th and
19th century
foundational works of
American literature.
H9. Identify and
explain the themes
found in a single
literary work; analyze
the ways in which
similar themes and
ideas are developed in
more than one literary
work.
West Virginia
RLA.O.12.1.03
RLA.O.11.1.03
RLA.O.10.1.03
RLA.O.9.1.03
Rating
1
Comments
Independent reading does not necessarily
mean that students will know a shared set
of foundational works.
RLA.O.10.1.08
1
West Virginia does expect students to
interpret themes, but ADP is more
specific in expecting students to also
analyze more universal themes that are
developed in different literary works.
This cross-comparison is not expected by
West Virginia.
Finding 3: In some cases, the alignment between the West Virginia 21st Century English
Language Arts Standards and the ADP Benchmarks rely completely or heavily on
standards from lower grade levels.
The ADP English Benchmarks are cumulative in nature and reflect what students should know
and be able to do upon high school graduation if they are to be prepared for success in college
and work. Some concepts in the ADP English Benchmarks—such as distinguishing fact from
opinion—which are typically found in state standards that fall below the high school level, are
taken into consideration in Achieve’s alignment analysis. West Virginia standards shaded in
blue in the accompanying side-by-side chart are those that were extracted from lower grades for
purposes of this analysis.
Some areas of alignment between the ADP English Benchmarks and content standards were
found at grades below 9-12. Some expectations are so essential to success in language arts that
they need to be reinforced at every grade level, and, particularly at the secondary levels, applied
to much more complex situations than they were in the lower grades. At the primary levels, for
example, students need to be taught how to use the context clues provided within a sentence to
figure out the definition of an unfamiliar word. As texts become more complex, however,
definitions of essential yet unfamiliar words may be found at the paragraph or section levels of a
text—a much more wide-ranging expectation of the use of context clues than that practiced at the
early grade levels.
TABLE 3 below indicates those areas of alignment between ADP and West Virginia that rely
entirely or heavily on standards from lower grades. The state may wish to consider including
these concepts in Grades 9-12 to ensure instruction in these areas.
TABLE 3 – Areas of Alignment that rely on the West 21st Century ELA Standards from
lower grade levels
ADP
West Virginia
Comments
RLA.O.2.1.05 Expectations related to giving/following directions
B1. Give and follow
Achieve Report
January 15, 2009
page 11
ADP
West Virginia
spoken instructions to
RLA.O.3.1.14
perform specific tasks, to
answer questions or to
solve problems.
RLA.O.3.3.01
RLA.O.4.3.01
B2. Summarize
RLA.O.12.1.06
information presented
RLA.O.11.1.06
orally by others.
RLA.O.10.2.07
RLA.O.9.2.08
RLA.O.3.3.01
B3. Paraphrase
RLA.O.4.3.01
information presented
RLA.O.10.2.07
orally by others.
RLA.O.9.2.08
F1. Follow instructions RLA.O.2.1.05
in informational or
RLA.O.3.1.14
technical texts to
perform specific tasks,
answer questions or
solve problems.
H5. Demonstrate
RLA.O.5.1.12
knowledge of metrics,
RLA.O.6.1.12
rhyme scheme, rhythm, RLA.O.7.1.09
alliteration and other
RLA.O.8.1.11
conventions of verse in
poetry.
Comments
appear much before Grades 9-12 and relate to written
directions rather than spoken directions.
Specific attention to summarizing information
presented orally is only evident at the elementary
levels.
Specific attention to summarizing information
presented orally is only evident at the elementary
levels.
Expectations related to giving/following directions
appear in Grades 2 and 3—not explicitly in Grades
9-12.
Expectations related to poetry reading appear below
Grades 9-12 in West Virginia.
Finding 4: Some of the expectations within the West Virginia 21st Century English
Language Arts Standards and in 21st Century Learning and Technology Standards
extend beyond the expectations set by the ADP Benchmarks by addressing concepts
that ADP does not explicitly address.
The ADP English Benchmarks include the content that postsecondary educators and employers
identified as essential skills for postsecondary success and the workplace. However, some
content and skills, such as creative writing or aesthetic analyses of literary works, that falls
outside of the focus of ADP is often included in high school English language arts classes and
may still be an appropriate focus of instruction in high school.
In addition, because they were written as end-of-high-school, or exit, benchmarks, the ADP
English Benchmarks do not include the level of detail that would be expected in a set of gradespecific content standards for English language arts. As a result, some of the specific content
included in the West Virginia 21st Century English Language Arts Standards in Grades 9-12 is
not included explicitly in the ADP Benchmarks. For example, West Virginia includes statements
on specific literary devices that are not explicitly stated in ADP. A greater degree of specificity
Achieve Report
January 15, 2009
page 12
within the West Virginia 21st Century English Language Arts Standards is to be expected
because they are intended to guide both instruction and assessment within the state.
On the other hand, some of the objectives in West Virginia that go beyond ADP address internal,
cognitive processes or strategies that may be more appropriate in a curricular document than a
set of performance expectations. For example, RLA.O.12.1.04 addresses reading strategies
(such as rereading, chunking, and activating prior knowledge) that may be difficult to observe
and measure. While they may be useful as learning tools, they may be less appropriate as
outcomes.
TABLE 4 – West Virginia 21st Century English Language Arts Standards that extend
beyond the ADP Benchmarks, by addressing concepts/performances not explicitly required
in the ADP Benchmarks
Grade 12
incorporate appropriate reading strategies necessary for a successful literary
experience, to gain information and perform an assigned task:
 rereading
 paraphrasing
RLA.O.12.1.04
 questioning
 analyzing
 chunking
 activating prior knowledge
demonstrate knowledge of and evaluate literary devices:
 archetypes
 allegory
 antithesis
 pace
 satire
RLA.O.12.1.07
 cadence
 scansion
 flashback
 foreshadowing
 Freytag’s pyramid (exposition, rising action, climax, falling action,
catastrophe)
use knowledge of the history, cultural diversity, politics, and effects of
RLA.O.12.1.10 language to comprehend and elaborate on the meaning of texts, to expand
vocabulary, and to draw connections to self and the real world.
research literary criticism and evaluate its applicability to the genre being
RLA.O.12.1.11
studied.
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strategically incorporate source material in a variety of ways, demonstrating a
sophisticated understanding of the ethics of writing:
 directly quoting
 paraphrasing
RLA.O.12.2.07
 summarizing
 using ellipses
<<Note that paraphrasing and summarizing are included in the context of
writing and in terms of the ethics of writing, which differs from ADP’s
statements on paraphrasing and summarizing.>>
adapt and use verbal and nonverbal strategies to listen for diverse purposes
 comprehension
 evaluation
 expression of empathy
RLA.O.12.3.03
 persuasion
 mediation
 collaboration
 facilitation
Grade 11
apply appropriate reading strategies necessary for a successful literary
experience, to gain information and perform an assigned task:
 rereading
 paraphrasing
RLA.O.11.1.04
 questioning
 analyzing
 chunking
 activating prior knowledge
demonstrate knowledge of and analyze the use of rhetorical and literary
devices:
 parallelism
 archetypes
 allegory
 parallel structure
 antithesis
 narrative pace
RLA.O.11.1.07
 satire
 cadence
 scansion
 flashback
 foreshadowing
 Freytag’s pyramid (exposition, rising action, climax, falling action,
catastrophe, denouement)
use knowledge of the history, cultural diversity, politics, and effects of
RLA.O.11.1.10 language to comprehend and elaborate on the meaning of texts, to expand
vocabulary, and to draw connections to self and to the real world.
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January 15, 2009
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RLA.O.11.1.11 research literary criticism related to the genre being studied.
recognize the concepts of intellectual property and plagiarism in all media:
 media copyright laws
RLA.O.11.2.03
 private/public domain
use verbal and nonverbal strategies to listen and respond for diverse
purposes:
 comprehension
 evaluation
RLA.O.11.3.03
 expression of empathy
 persuasion
 mediation
 collaboration
Grade 10
RLA.O.10.1.02 compare and contrast literary styles according to genre.
RLA.O.10.1.04 apply various pre-reading skills and comprehension strategies for activating
prior knowledge and asking questions during reading and post reading for
 literary experience
 examining textual information
 performing an assigned task
interpret and explain the author’s choice of literary devices used to construct
meaning and define the author’s/reader’s purpose:
 symbolism
 imagery
 irony
 satire
RLA.O.10.1.07
 cadence
 scansion
 flashback
 foreshadowing
 Freytag’s pyramid (exposition, rising action, climax, falling action,
catastrophe, denouement)
adapt and use active listening strategies to evaluate the message, formulate a
strategy and respond to
 intended purpose
RLA.O.10.3.04
 make predictions
 construct meaning from discussion, speech, or media
 critique presentation
Grade 9
RLA.O.9.1.02 recognize literary styles according to genre.
use various pre-reading skills and comprehension strategies for activating
RLA.O.9.1.04 prior knowledge or generating questions during reading and post reading,
literary experience, information and/or performing a task.
explain the literary devices used to construct meaning and define the
RLA.O.9.1.07
author’s/reader’s purpose:
Achieve Report
January 15, 2009
page 15
RLA.O.9.3.04
 symbolism
 imagery
 simile
 humor
 rhythm
 meter
 assonance
use active listening strategies to analyze the message, formulate a response
and react to
 determine purpose
 make predictions
 differentiate fact from opinion
 construct meaning of discussion, speech, or media
West Virginia 21st Century Learning and Technology Standards not included in ADP
The West Virginia 21st Century Learning and Technology Standards include two types of
statements—expectations for technology skills and dispositions for learning. These statements
were written for a different purpose than the ADP English Benchmarks. The ADP English
Benchmarks were written to describe knowledge and skills in English and communications
(listening, speaking, reading, writing, viewing, producing media, and using critical thinking). As
a result, areas of non-alignment are expected between the two documents, as the West Virginia
statements are much more detailed in terms of the specific technologies with which students are
expected to have skill and in terms of the learning dispositions students are expected to display.
It is important to note that some of the 21st Century Learning and Technology Standards that are
included in the side-by-side chart as aligning with ADP align only partially with ADP. For
example, objective 21C.O.9-12.1.TT6—“Student uses advanced features and utilities of
spreadsheet software, (e.g., formulas, filters, pivot tables, pivot charts, macros, conditional
formatting), to perform calculations and to organize, analyze and report data”—aligns with ADP
A7—“Comprehend and communicate quantitative, technical and mathematical information”—in
that it emphasizes the communication of quantitative, technical, and mathematical information.
The specific functions involved in using spreadsheets, however, are not a part of ADP. This
partial alignment is true for many of the technology objectives that appear in the side-by-side
chart. The purposes for which students use the technology align with ADP, but the specifics of
their use of the functions of technology do not align since ADP approaches technology much
more generally as an area of knowledge. The aspects of the statement that align with ADP are
highlighted in yellow in the side-by-side chart.
One concern with the technology learning objectives is that they often describe dispositions or
behaviors that may pose measurability challenges for the state. For example, it may be difficult
to measure reliably if students are visualizing “the connection between seemingly unrelated
ideas” and producing solutions that are “fresh” (21C.O.9-12.2.LS) or if a student can “help
others stay focused” (21C.O.9-12.3.LS5). It may also be difficult to observe if “prior to
beginning work, student reflects upon possible courses of action and their likely consequences”
(21C.O.9-12.3.LS6).
Achieve Report
January 15, 2009
page 16
A second concern with the 21st Century Learning and Technology Standards is that although
they describe worthy goals for all students, secondary content teachers may not regard these
skills and dispositions to be their responsibility. Without a “home” within the curriculum as part
of a set of content expectations, content teachers may not take ownership of these standards.
Content teachers may need professional development support and incentive in order to make
these learning and technology standards a part of the required curriculum for all high school
graduates
TABLE 5 – West Virginia 21st Century Learning and Technology Standards
that extend beyond the ADP Benchmarks, by addressing concepts/performances not
explicitly required in the ADP Benchmarks.
Learning Skills Objectives
Student engages in a critical thinking process that supports synthesis and
21C.O.9-12.2.LS1
conducts evaluation using complex criteria.
Student engages in a problem solving process by formulating questions and
21C.O.9-12.2.LS3
applying complex strategies in order to independently solve problems.
Student visualizes the connection between seemingly unrelated ideas and
independently produces solutions that are fresh, unique, original and well
21C.O.9-12.2.LS4 developed. Student shows capacity for originality, concentration,
commitment to completion, and persistence to develop unique and cogent
products.
Student remains composed and focused, even under stress, willingly aligns
his/her personal goals to the goals of others when appropriate, approaches
21C.O.9-12.3.LS1
conflict from win-win perspective, and derives personal satisfaction from
achieving group goals.
Student independently considers multiple perspectives and can represent a
problem in more than one way, quickly and calmly changes focus and goals
21C.O.9-12.3.LS2
as the situation requires, and actively seeks innovations (e.g. technology)
that will enhance his/her work.
Student demonstrates ownership of his/her learning by setting goals,
monitoring and adjusting performance, extending learning, using what
21C.O.9-12.3.LS3
he/she has learned to adapt to new situations, and displaying perseverance
and commitment to continued learning.
Student maintains a strong focus on the larger project goal and frames
appropriate questions and planning processes around goal. Prior to
beginning work, student reflects upon possible courses of action and their
21C.O.9-12.3.LS6 likely consequences; sets objectives related to the larger goal; and
establishes benchmarks for monitoring progress. While working on the
project, student adjusts time and resources to allow for completion of a
quality product.
Technology Tools Objectives
Student routinely applies keyboarding skills, keyboard shortcut techniques,
21C.O.9-12.1.TT2
and mouse skills with facility, speed and accuracy.
21C.O.9-12.1.TT3 Student uses advanced utilities (e.g., zipping or compressing files, file level
Achieve Report
January 15, 2009
page 17
21C.O.9-12.1.TT5
21C.O.912.1.TT11
21C.O.9-12.2.TT1
21C.O.9-12.2.TT4
21C.O.9-12.3.TT1
21C.O.9-12.3.TT3
21C.O.9-12.3.TT6
21C.O.9-12.3.TT7
anti-virus scans), converts files to different formats (e.g., .doc, .xls, .mdb,
.htm, .pdf) and saves finished products to multiple media sources (e.g.,
CDRW, DVDR, USB drives, shared folders, web-based file storage).
Student uses advanced features of word processing software (e.g., outline,
table of contents, index feature, draw tool, headers and footers, track
changes, macros, hyperlinks to other file formats, etc.).
Student imports and exports multiple data formats and integrates to multiple
productivity programs (e.g., exports comma delimited files, standard data
formats) and understands transferability of data among different programs.
Student knows how to find information necessary to solve advanced
problems related to hardware, software, networks, and connections (e.g., by
accessing online help, Internet searches, technical documentation, system
utilities, and communication with technical experts).
Student uses technology tools and multiple media sources to analyze a realworld problem, design and implement a process to assess the information,
and chart and evaluate progress toward the solution.
Student protects software, hardware and network resources from viruses,
vandalism, and unauthorized use and employs proper techniques to access,
use and shut down technology equipment.
Student evaluates current trends in information technology, discusses the
potential social, ethical, political, and economic impact of these
technologies, and analyzes the advantages and disadvantages of widespread
use and reliance on technology in the workplace and society.
Student evaluates and applies technology tools for research, information
analysis, problem solving, content learning, decision making, and lifelong
learning.
Student protects his/her identity online and in email and/or websites, limits
the distribution of personal information/pictures, and evaluates the
authenticity of emails that solicit personal information. Student identifies
the methodologies that individuals and businesses can employ to protect the
integrity of technology systems.
Recommendations for Improvement:
o Consideration should be given to strengthening the expectations regarding logic in the
English language arts standards. ADP Benchmarks focus quite clearly on logical
arguments, both read and produced, and this is an area that is also a major part of the
NAEP Reading Framework for 2009 and the NAEP Writing Framework for 2001. The
importance of a student being able to be critical of what is presented in text or in other
media and the ability to construct cogent arguments are clearly skills necessary for
success no matter what the student’s postsecondary plans may be. Providing specific
expectations in this area would enrich the state’s standards.
o West Virginia’s 21st Century Learning Skills and Technology Tools Content Standards
and Objectives draw much needed attention to the skills that are needed for success in
this new century. Rather than call out such expectations in a document separate from its
Achieve Report
January 15, 2009
page 18
content expectations, however, Achieve has chosen to include some of these standards
within the areas of mathematics and English language arts. The concern with listing such
expectations outside of a content area is that secondary teachers may not regard them as
part of their content responsibility. As long as care has been taken to assure that these
skills fall within the purview of the teachers and the teachers are provided the necessary
professional development support and incentive to address these standards, the state’s
choice to separate these expectations from the content areas may be successful.
Achieve Report
January 15, 2009
page 19
MAJOR FINDINGS & RECOMMENDATIONS:
MATHEMATICS
Overview
For purposes of this analysis, Achieve staff constructed a side-by-side chart comparing
Achieve’s American Diploma Project (ADP) Mathematics Benchmarks with the 21st Century
Mathematics Content Standards and Objectives for West Virginia Schools. In addition, the 21st
Century Learning Skills (LS) And Technology Tools (TT) Content Standards And Objectives For
West Virginia Schools were included, but only when relevant to the mathematical content and
only for Grades 9-12. The Achieve study focused on West Virginia’s high school standards for
the courses selected by state representatives. However, since the ADP Benchmarks are
cumulative in nature, objectives from middle school were used to complete the chart in some
instances. Commentary regarding rigor can be found in both this summary report and in the
comments in the fourth column of the side-by-side chart.
For this analysis, state representatives requested that the objectives from only the following high
school course be included: Algebra I (A1), Algebra II (A2), Geometry (G), and Trigonometry
(T). In some instances objectives exist in Conceptual Mathematics (CM), Pre-calculus (PC), and
Probability and Statistics (PS), which may be relevant to the alignment. While alignment ratings
were not influenced by objectives from these courses, they may be referenced in this report and
in the commentary column of the side-by-side chart in cases where alignment ratings could be
improved with their inclusion.
Effective in the 2010-2011 academic year, the West Virginia requirement for high school
graduation is four credits, with at least three mathematics classes in Grades 9-12. While the
recommended course sequence for students in the professional pathway is Algebra I, Geometry,
Algebra II, Trigonometry, and Pre-Calculus, students in the skilled pathway are recommended to
take Algebra I, Geometry, Conceptual Mathematics, and College Transition Mathematics or
Algebra II. The West Virginia State Board of Education’s recently adopted legislation indicates
that there are additional alternatives available for students who struggle with Algebra I. This
may include a pairing of courses in one year, which may be counted as two credits of
mathematics. These alternative sequences are likely to have a reduced level of rigor when
compared with the professional pathway. It is therefore not clear whether a student following an
alternative path would be prepared for entry-level mathematics in college. For this analysis,
West Virginia has requested that Algebra I, Geometry, Algebra II, and Trigonometry be
considered. Since there are multiple courses and course sequences available to West Virginia
students, the state is advised to carefully analyze and adjust the requirements of alternate courses
and course sequences when compared with the Algebra I, Geometry, Algebra II, and
Trigonometry sequence to ensure those students who opt for alternative routes are prepared for
future work and/or study.
Alignment Analysis
Overall, there is a good alignment between the ADP Benchmarks and the 21st Century
Mathematics Content Standards and Objectives for West Virginia Schools. The 21st Century
Achieve Report
January 15, 2009
page 20
Learning Skills (LS) and Technology Tools (TT) Content Standards and Objectives for West
Virginia Schools were used to enhance alignment of the Content Standards and Objectives where
applicable. With these three sets of standards, West Virginia joins 16 states that have completed
the alignment process and emerged with a similar Common Core of college- and career-ready
standards that align with a critical subset of the ADP mathematics Benchmarks.3 Of the 34
Common Core Mathematics Benchmarks, the West Virginia standards meet 29 of them. In its
Algebra I, Geometry, Algebra II, Trigonometry sequence, there is no mention of modeling with
exponential functions (ADP J5.4) or evaluating reports based on data (L2.1), two ADP Common
Core concepts. In the area of geometry, proof and construction are addressed in the West
Virginia standards but not clearly and specifically related to parallel and perpendicular lines, as
is done in ADP, resulting in a weak alignment with these Common Core Mathematics
Benchmarks. West Virginia also provides weak treatment of the use of special symbols of
mathematics.
In addition, there are instances where the alignment required use of West Virginia objectives
from middle grades (in blue font in the side-by-side chart). In instances where alignment to the
ADP Benchmarks comes solely from middle grades, there may be some concern that the level of
rigor is not comparable.
Most of the ADP Benchmarks have at least one West Virginia objective that aligns with each
Benchmark, but the strength of that alignment, as noted by the numerical rating system used in
the side-by-side chart, varies somewhat. On the flip side of this comparison, it is also the case
that the majority of West Virginia objectives can be found in the ADP Benchmarks.
The 21st Century Mathematics Content Standards and Objectives for West Virginia Schools and
21st Century Learning Skills (LS) And Technology Tools (TT) Content Standards And Objectives
For West Virginia Schools define rigorous expectations which generally align well with the ADP
Benchmarks with some exceptions. What follows is a description of some general
commonalities and differences found between the West Virginia and ADP sets of standards.
Finding 1: While the overall alignment is good between the West Virginia standards
and the ADP Benchmarks, there are several instances where ADP Benchmarks do not
have a counterpart in the 21st Century Mathematics Content Standards and Objectives
for West Virginia Schools or in the 21st Century Learning Skills (LS) and Technology
Tools (TT) Content Standards and Objectives For West Virginia Schools.
There are some ADP Benchmarks that are either not addressed in the West Virginia objectives or
that are not addressed as explicitly as they could. A few concepts found in the ADP
Benchmarks—such as using geometric series and exponential functions as mathematical models
and evaluation of statistical reports—are not addressed at all in the West Virginia objectives.
TABLE 1 below shows the ADP Benchmarks which have no counterparts in the 21st Century
Mathematics Content Standards and Objectives for West Virginia Schools. Ratings of “0” were
assigned in the accompanying side-by-side chart since there is no match for these ADP
Benchmarks. Some of the following ADP Benchmarks have an * following their designation.
3
Out of Many, One: Toward Rigorous Common Core Standards from the Ground Up, Achieve, July
2008, page 8, Table 2: ADP Core in Mathematics. See http://www.achieve.org/node/1019.
Achieve Report
January 15, 2009
page 21
These “asterisked” benchmarks are recommended for all students but required only for those
students intending to pursue a mathematics-intensive course of study or career. Some of the
following ADP Benchmarks also have the designation [ADP Core] at the end. ADP Core
Benchmarks are those which at least 75 percent of ADP Network States have included in their
standards documents.
TABLE 1 – ADP Benchmarks that are not addressed in the 21st Century Mathematics
Content Standards and Objectives for West Virginia Schools or in the 21st Century
Learning Skills (LS) And Technology Tools (TT) Content Standards And Objectives
For West Virginia Schools
Algebra
J5.4. Recognize and solve problems that can be modeled using an exponential function, such as
compound interest problems.
[ADP Core]
J5.6. Recognize and solve problems that can be modeled using a finite geometric series, such as
home mortgage problems and other compound interest problems.
J6. * Understand the binomial theorem and its connections to combinatorics, Pascal’s triangle
and probability.
Data Interpretation, Statistics and Probability
L2.1. Evaluate reports based on data published in the media by considering the source of the
data, the design of the study, and the way the data are analyzed and displayed.
[ADP Core]
L2.3. Recognize when arguments based on data confuse correlation with causation.
L3.3. Explain the differences between randomized experiments and observational studies.
L4.3. Explain how the law of large numbers can be applied in simple examples.
Mathematical Reasoning
MR7. Recognizing and using the process of mathematical modeling: recognizing and clarifying
mathematical structures that are embedded in other contexts, formulating a problem in
mathematical terms, using mathematical strategies to reach a solution, and interpreting the
solution in the context of the original problem.
MR9. Shifting regularly between the specific and the general, using examples to understand
general ideas, and extending specific results to more general cases to gain insight.

Finding 2: There are some instances where the alignment between the 21st Century
Mathematics Content Standards and Objectives for West Virginia Schools and the 21st
Century Learning Skills (LS) And Technology Tools (TT) Content Standards And
Objectives For West Virginia Schools and the ADP Benchmarks is not as complete or
not as clear and explicit as it could be.
While in one sense there is good alignment between West Virginia objectives and the ADP
Benchmarks—with one or more objectives aligning with most of the benchmarks—Achieve
reviewers identified areas where they believe the alignment could be enhanced. In some
instances, there is some degree of alignment between the West Virginia objectives and the ADP
Benchmarks, but there are gaps with respect to content or performance expectations and/or subtle
differences in the expectations. For example, geometric proof is required in a general way but
without reference to specific theorems related to parallel lines and angles. Weak ratings and/or
Achieve Report
January 15, 2009
page 22
comments in the chart indicate gaps in content or performance alignment, or what appear to be
differences in the level of expectation, given the wording used in West Virginia. Those cases
where the full expectation defined in an ADP Benchmark is not covered completely or well by
the West Virginia objectives are indicated in TABLE 2 with a rating of “1” or, in a few cases, a
“2.” In other instances, content from the ADP Benchmarks is only addressed in objectives that
may not be accessible to all students. Since the West Virginia high school graduation
requirements offer multiple pathways, it is not clear that all content is intended for all students.
Even though some aligning objectives received a high rating, there may be some question
regarding the level of access to the content for students. Reviewer comments related to this are
captured in the side-by-side chart and also in TABLE 2 below.
TABLE 2 – ADP Benchmarks that are not explicitly or completely addressed in the 21st
Century Mathematics Content Standards and Objectives for West Virginia Schools and the
21st Century Learning Skills (LS) And Technology Tools (TT) Content Standards And
Objectives For West Virginia Schools
ADP
West Virginia
Rating
Comments
A Pre-Calculus standard (M.O.PC.2.6) is needed to
match this asterisked ADP Benchmark addressing
series formulas. Though the Alg I and II standards
M.O.A1.2.5
1
show development of these important concepts, they
J1.7*
M.O.A2.2.16
neglect the derivation and use of formulas related to
series in general and the infinite geometric series in
particular.
Theorems specifically addressing parallel lines are not
in the West Virginia objectives. The only reference to
geometric constructions is to triangle medians,
M.O.G.3.5
1
K2.1
altitudes, and angle and perpendicular bisectors. It is
M.O.G.3.6
not clear that formal construction with compass and
straightedge is required in West Virginia.
While these West Virginia objectives address proof
and construction in general, they are specifically
M.O.G.3.5
1
K2.2
aimed at specific types of angles and the parts of
M.O.G.3.18
triangles.
Conditional probability is not included in West
2
Virginia. Alignment here relies on middle school
L4.4
M.O.8.5.2
standards.
Only specific notations are required in West Virginia,
like these A2 standards that address interval notation
M.O.A2.2.7
(there are others in A3 as well as references to sigma
M.O.A2.2.9
1
MR4
and set notation in PC). There is no clear call for
M.O.A2.2.13
general use of correct notation or terminology in West
Virginia.
Precision of results is not addressed in the West
2
Virginia objectives. Here alignment relies on middle
MR5
M.O.8.1.3
school standards.
1
West Virginia objectives for A1, G, A2, and
MR6
21C.O.9Achieve Report
January 15, 2009
page 23
12.2.TT4
Trigonometry do not address this problem solving
process standard. The Technology Tools standard
does not clearly address sorting relevant and irrelevant
information and specifies technology use.
In addition, there are a few non-asterisked ADP Benchmarks that rely on West Virginia
objectives from Algebra II or Trigonometry for the alignment. As not all West Virginia students
are required to take Algebra II and Trigonometry, these gaps are important to note. They include
the following:




J2.3 – M.O.A2.2.7: Function notation and evaluation of a function at a point in its
domain
J4.4 – M.O.A2.2.10: Graphing a linear inequality
K11.3 – M.O.T.3.9: Using trigonometric formulas for area measure of a triangle
MR4 – M.O.A2.2.7, 9, 13: Correct and precise use of the notation of mathematics
Finding 3: There are several areas of alignment between the ADP Benchmarks and the
21st Century Mathematics Content Standards and Objectives for West Virginia Schools
that rely completely or heavily on middle grade objectives.
When the expectations from high school are considered, alignment with the ADP Benchmarks is
generally strong but with some significant exceptions that will be noted in this report. Most of
the ADP Benchmarks have one or more objectives that align with them to some degree. As
shown in the side-by-side chart accompanying this report, in select instances Achieve also
included expectations from middle grade standards. This is because the ADP Benchmarks are
cumulative in nature and reflect what students should know and be able to do upon high school
graduation if they are to be prepared for success in college and work. Some concepts in the ADP
Benchmarks—such as number theory and order of operations—are most typically found in state
standards in the middle school grades and are taken into consideration in Achieve’s alignment
analysis. In some cases, this may be appropriate, while in others it may suggest a lack of rigor.
For example computation with rational numbers, including rates and proportions, is addressed in
Grade 8. This may be appropriate since it could be assumed that these skills would be reinforced
in high school mathematics courses. However, ADP L4.4, the application of probability, such as
conditional and independent events, is also addressed only in Grade 8, whereas this concept is
deserving of emphasis in high school mathematics at a more rigorous level than in middle
school.
TABLE 3 below indicates those alignments between the ADP Benchmarks and West Virginia
21st Century Mathematics Content Standards that rely entirely or heavily on middle school
objectives. Objectives noted in blue font in the accompanying side-by-side chart are those that
were extracted from middle grades for purposes of this analysis.
TABLE 3 – Areas of Alignment that rely on West Virginia objectives that fall below the
high school level
ADP West Virginia
Comments
Number Sense and Numerical Operations
Achieve Report
January 15, 2009
page 24
ADP
I1.1
I1.2
I1.3
I1.4
I1.5
I2.1
I2.2
I3
J2.1
J4.1
K8.1
K8.3
K9
L1.2
L1.3
L1.4
L2.2
L3.1
L3.2
L4.1
L4.2
L4.4
L4.5
West Virginia
Comments
Operations
with
rational
numbers
M.O.8.1.3
Ratios and proportions
M.O.8.1.3
M.O.8.2.2
Order of operations
M.O.7.2.2
Basic Number Theory
M.O.6.1.2
Problem solving (and computation) with numbers in scientific
M.O.8.1.2
notation
M.O.7.1.7
Absolute value
M.O.7.1.1
M.O.7.2.2
Comparison of real numbers
M.O.7.1.1
Extension of number systems
M.O.7.1.1
M.O.8.1.1
M.O.A2.2.3
Algebra
M.O.A2.2.7 Functions
M.S.6.2
Linear equations and slope
M.O.8.2.6
M.O.A1.2.6
M.O.A1.2.8
Geometry
Units of measure
M.S.8.4
M.O.7.4.3
Scale and measurement
M.O.7.3.5
M.O.G.3.16 Visualization and representation of two-dimensional and threedimensional shapes
M.O.5.3.2
Data Interpretation, Statistics and Probability
M.O.A1.2.19 Tables, charts, and graphs
M.O.7.5.3
Summary statistics, including measures of center and spread
M.O.8.5.5
Data comparisons
M.O.7.5.4
Misleading uses of data
M.O.8.5.5
Impact of sampling methods, bias, and question phrasing on data
M.O.8.5.4
collection and conclusions
M.O.A1.2.20 Misleading uses of data
M.O.6.5.2
21C.O.912.1.TT8
How probability quantifies the likelihood of an event
M.O.6.5.3
Frequency and its relationship to probability
M.O.7.5.2
M.O.7.5.3
Conditional probability
M.O.8.5.2
Practical probability uses
M.O.8.5.4
Achieve Report
January 15, 2009
page 25
ADP
MR5
MR8
West Virginia
M.O.6.5.3
M.O.A1.2.18
M.O.A1.2.20
M.O.8.1.3
M.O.8.1.3
M.O.8.2.2
M.O.A1.2.2
21C.O.912.2.LS3
21C.O.912.2.TT4
Comments
Mathematical Reasoning
Precision of results
Reasonableness of a solution
Finding 4: Some of the expectations within the 21st Century Mathematics Content
Standards and Objectives for West Virginia Schools extend beyond the expectations set
by the ADP Benchmarks for all students.
In some instances, West Virginia objectives in this course sequence (Algebra I, Geometry,
Algebra II, Trigonometry) address content that is not addressed at all by the ADP Benchmarks.
It is not clear that all students are indeed expected to take all of the courses in this sequence, so
the inclusion of standards not addressed in the ADP benchmarks—particularly in
Trigonometry—is not totally unexpected. It is important that the state take steps to define which
expectations from high school are expected of all students and which are expected only of
students intending to pursue mathematically intensive college programs and careers.
TABLE 4 below identifies the West Virginia objectives that extend beyond the ADP
Benchmarks or that define concepts or performances not explicitly addressed in the ADP
Benchmarks. They received an asterisk-rating on the side-by-side chart. (Note: The West
Virginia objectives are organized in the table below by ADP strand as they occur in the
accompanying side-by-side chart, rather than sequentially as they appear in the West Virginia
standards document.)
TABLE 4 – 21st Century Mathematics Content Standards and Objectives for West Virginia
Schools that extend beyond the ADP Benchmarks or that include concepts/performances
not explicitly addressed in the ADP Benchmarks (organized by ADP strand from the
accompanying side-by-side chart)
West
Topic
Virginia
Comments
Standard
Number Sense and Numerical Operations
Polar form of
ADP does not require expression, operation, or graphing of complex
complex
M.O.T.3.10 numbers in polar form.
numbers
Achieve Report
January 15, 2009
page 26
Topic
West
Virginia
Standard
Comments
Algebra
In addition to the concept of function families, this West Virginia
Families of
M.O.A2.2.8 standard specifically references radical, step and piece-wise
functions
functions.
Quadratic
ADP does not require solutions for quadratic inequalities.
M.O.A2.2.9
inequalities
Variations M.O.A2.2.11 ADP does not include inverse or joint variations.
Periodic and
ADP does not require modeling with periodic data.
parametric M.O.T.3.7
models
Polynomial
ADP does not require problem solving with polynomial functions.
M.O.A1.2.11
applications
This standard may be more appropriate for Alg II.
Vectors
M.O.T.3.11 ADP does not require vector application problems.
Geometry
Analysis of M.O.G.3.8 ADP does not specifically require analysis or measurement of
polygons M.O.G.3.14 polygons.
Trigonometric
ADP does not require solutions for trigonometric equations.
M.O.T.3.4
equations
Inverse
M.O.T.3.5
trigonometric
ADP does not require inverse trigonometric functions.
M.O.T.3.6
functions
In addition, the West Virginia standards include some objectives that, while they align well with
the ADP Benchmarks, include some aspects that extend beyond ADP expectations. Rather than
receiving an asterisk rating, these alignments are noted by a “2*” or “3*” rating in the side-byside chart. Topics that correspond to such ratings include:














Operations with complex numbers (I3)
Deriving the laws of exponents (J1.1)
Solving equations involving radicals and exponents (J1.2*)
Analysis of the relationship between factored forms of polynomials and their graphs
(J1.4)
Finding the range of a function (J2.2*)
Quadratic solutions over the set of complex numbers (J3.5)
Systems of inequalities (J4.4)
Using graphs to analyze solutions to quadratic problems (J4.5)
Problem solving and transformations in relation to conic sections (J4.6)
The relationship between exponential graphs and their equations (J4.7)
Modeling with linear inequalities (J5.1)
Using matrices to solve a system of equations (J5.2)
Quadratic solutions over the set of complex numbers (J5.3)
The triangle inequality theorem (K1.2)
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


Approximation of the area of irregular shapes (K8.2)
Midpoint formula (K10.3)
Inverse trig functions (K12.3*)
Quadratic regressions (L3.4)
Finally, it is also the case that selected West Virginia objectives align with those ADP
Benchmarks that, while recommended for all students, are identified as required only for those
students intending to take calculus in college—designated in the ADP Benchmarks by an asterisk
(e.g., K10.4*). This is an issue in West Virginia since the state does not make any such
distinction between objectives for all students and objectives for students intending to pursue
mathematically-intensive fields of work or study. The West Virginia Standards simply define
expectations for high school, with no differentiation based on postsecondary plans. While nearly
all asterisked ADP Benchmarks align with West Virginia objectives from Algebra II or
Trigonometry, West Virginia educators need to examine the high school standards that align with
asterisked ADP Benchmarks and determine whether they believe these define content that is
important for all students or only for students intending to continue with advanced mathematics
study. The side-by-side chart that accompanies this report will be a helpful tool in analyzing
more carefully the standards that fall into this category.
TABLE 5 below lists the West Virginia objectives that align with asterisked ADP Benchmarks.
In cases where only a portion of an objective aligns with an asterisked benchmark, that portion is
bolded and underlined below. If no bolding or underlining exists, then the entire objective is
deemed to align with an asterisked benchmark. The objectives are organized by ADP strand as
they occur in the accompanying side-by-side chart, rather than sequentially as they appear in the
West Virginia standards document.
TABLE 5 – 21st Century Mathematics Content Standards and Objectives for West Virginia
Schools that align with asterisked ADP Benchmarks (organized by ADP strand from the
accompanying side-by-side chart).
Related ADP
Algebra
Benchmark
M.O.A2.2.4 simplify expressions involving radicals and fractional exponents,
convert between the two forms, and solve equations containing radicals and
J1.2*
exponents.
M.O.A1.2.5 analyze a given set of data and prove the existence of a pattern
numerically, algebraically and graphically, write equations from the patterns
and make inferences and predictions based on observing the pattern.
J1.7*
M.O.A2.2.16 describe and illustrate how patterns and sequences are used to
develop recursive and closed form equations; analyze and describe
characteristics of each form
M.O.A2.2.7 define a function and find its zeros; express the domain and
range using interval notation; find the inverse of a function; find the value of
J2.2*
a function for a given element in its domain; and perform basic operations on
functions including composition of functions.
M.O.A2.2.7 define a function and find its zeros; express the domain and
J2.4*
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J2.5*
J2.6*
J3.4*
J4.6*
J5.5*
Related ADP
Benchmark
K10.4*
K12.1*
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range using interval notation; find the inverse of a function; find the value of a
function for a given element in its domain; and perform basic operations on
functions including composition of functions.
M.O.A2.2.7 define a function and find its zeros; express the domain and
range using interval notation; find the inverse of a function; find the value of
a function for a given element in its domain; and perform basic operations on
functions including composition of functions.
M.O.A2.2.14 define a logarithmic function, transform between exponential
and logarithmic forms, and apply the basic properties of logarithms to
simplify or expand an expression.
M.O.A2.2.6 develop and use the appropriate field properties of matrices by
adding, subtracting, and multiplying; solve a system of linear equations
using matrices; and apply skills toward solving practical problems.
M.O.A2.2.12 analyze the conic sections; identify and sketch the graphs of a
parabola, circle, ellipse, and hyperbola and convert between graphs and
equations.
M.O.A1.2.15 describe real life situations involving exponential growth and
decay equations including y=2x and y=(½)x; compare the equation with
attributes of an associated table and graph to demonstrate an understanding of
their interrelationship.
M.O.A2.2.14 define a logarithmic function, transform between exponential
and logarithmic forms, and apply the basic properties of logarithms to
simplify or expand an expression.
Geometry
M.O.A2.2.12 analyze the conic sections; identify and sketch the graphs of a
parabola, circle, ellipse, and hyperbola and convert between graphs and
equations.
M.O.T.3.1 apply the right triangle definition of the six trigonometric
functions of an angle to determine the values of the function values of an
angle in standard position given a point on the terminal side of the angle.·
determine the value of the other trigonometric functions given the value of
one of the trigonometric functions and verify these values with technology.·
using geometric principles and the Pythagorean Theorem, determine the six
function values for the special angles and the quadrantal angles and use them
in real-world problems.· compare circular functions and the trigonometric
function values to draw inferences about coterminal angles and co-functions.
M.O.T.3.2 convert angle measures from degrees to radians (and vice
versa) and apply this concept to· create a data set, analyze, and formulate a
hypotheses to test and develop formulas for the arclength, area of a sector,
and angular velocity and use the formula for application in the real-world.·
compare and contrast the concepts of angular velocity and linear velocity
and demonstrate by graphical or algebraic means relationship between
them and apply to real-world problems.
M.O.G.3.13 investigate measures of angles formed by chords, tangents, and
secants of a circle and draw conclusions for the relationship to its arcs.
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K12.2*
K12.3*
K12.4*
M.O.T.3.3 using various methods, basic identities and graphical
representation· verify trigonometric identities· prove the sum and difference
to two angles, double-angles, and half-angle identities
M.O.T.3.6 identify a real life problem utilizing graphs of trigonometric
functions and/or the inverse functions; make a hypothesis as to the outcome;
develop, justify, and implement a method to collect, organize, and analyze
data; generalize the results to make a conclusion; compare the hypothesis and
the conclusion; present the project using words, graphs, drawings, models, or
tables.
M.O.T.3.8 investigate real-world problems within a project based
investigation involving triangles using the trigonometric functions, the law of
sines and the law of cosines, justify and present results.
Recommendations for improvement:
o Consideration should be given to the commentary Achieve has provided in this report on
areas where alignment of the Algebra I, Geometry, Algebra II, and Trigonometry
standards from the 21st Century Mathematics Content Standards and Objectives for West
Virginia Schools with the ADP Benchmarks can be made even stronger and clearer.
While some of the ADP Benchmarks are not addressed in the West Virginia objectives, it
is also the case that alignment of some West Virginia objectives with the ADP
Benchmarks appears weak or unclear, leading to differences in the level of expectation of
the two sets of standards. Consideration should be given to including more specific
references in the high school standards to mathematical modeling, particularly in
exponential and series models. Consideration should also be given in geometric proof to
specifying which types of theorems are to be proved, such as those related to parallel and
perpendicular lines. A third area where large improvements can be made is in the area of
evaluation of reports based on statistical analysis, including issues with sampling and
bias.
o The rigor and requirements of the 21st Century Mathematics Content Standards and
Objectives for West Virginia Schools and the 21st Century Learning Skills (LS) And
Technology Tools (TT) Content Standards And Objectives For West Virginia Schools for
all students, as well as for students preparing for mathematics-intensive college majors
and careers, is unclear. Graduation requirements and course sequences that meet these
graduation requirements need to be clarified to ensure that all students meet the minimum
requirement for success in college and careers. The present established requirements are
not clearly linked to courses that will necessarily meet the needs of students as they exit
West Virginia high schools. In some cases, objectives from other courses, such as
Conceptual Mathematics, College Transition Mathematics, or Algebra III, could fill gaps
in the alignment. In addition, the alternative (equivalent) courses to Algebra I and
Algebra II should be analyzed for alignment and gaps with the recommended West
Virginia course sequence.
o As steps are taken to define the mathematics that is important for all students and for
calculus-intending students, care should also be taken to determine whether there is
content included in Algebra II and Trigonometry that can be deleted. The Trigonometry
objectives contain a significant amount of content that is not included in the ADP
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Benchmarks at all—such as inverse trigonometric functions, periodic and parametric
models, vector applications, and using matrices—and a meaningful discussion among
state mathematics educators and mathematicians could be had to determine whether such
content should indeed be in the West Virginia state standards. It may be the case that
only calculus-intending students are expected to take Trigonometry, but this should be
clarified.
********
Conclusion
Overall, this review found alignment to be good between the West Virginia Standards and the
ADP Benchmarks. Consideration should be given to the commentary Achieve has provided in
this report on areas where alignment can be made even stronger and clearer such as in the area of
Logic in English and modeling, geometric proof and the evaluation of reports based on statistical
analysis in mathematics. This report also suggests that because West Virginia’s 21st Century
Learning Skills and Technology Tools Content Standards and Objectives draw much needed
attention to the skills that are needed for success in this new century, the state may want to
include some of these specific expectations within the English and mathematics content areas to
ensure that they are the focus of instruction. Finally, in mathematics, graduation requirements
and course sequences need to be clarified and aligned to ensure that all students including those
following an alternative pathway will be prepared to meet the minimum requirement for success
in college and careers.
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APPENDIX A: BIOGRAPHIES
The following Achieve staff and consultants in mathematics led the analysis and report
development for West Virginia.
ACHIEVE STAFF
JOANNE THIBAULT ERESH, SENIOR ASSOCIATE, ENGLISH LANGUAGE ARTS, ACHIEVE
JoAnne Thibault Eresh is a senior associate at Achieve, where she leads the English language
arts aspects of the reviews of standards and assessments. She taught writing at the university
level and English at public and private high schools in St. Louis, Mo., and in Fitchburg, Mass.
She began her work in curriculum design and performance assessment in 1979 under
Superintendent Richard C. Wallace, Jr., and from 1981 to 1994 was director of the Division of
Writing and Speaking for the Pittsburgh Public Schools. During that time, she directed The
Pittsburgh Discussion Model Project, funded by the Rockefeller Foundation and part of the
CHART network, and she later directed the imaginative writing part of the ARTS Propel Project,
a joint project with Harvard’s Project Zero and the Educational Testing Service. She was the
Pittsburgh district coordinator for the New Standards Project and wrote the teachers’ guides for
the New Standards ELA Portfolios. In 1995, she was one of the original resident fellows at the
Institute for Learning at the University of Pittsburgh’s Learning Research and Development
Center. She also coordinated the New Standards Linking Projects. From 1997 to March 2001,
she was the coordinator of staff development in Community District Two in New York City
where she was responsible for the hiring, training, and coordination of that district’s staff
development group. JoAnne holds a bachelor’s degree in English from Webster College in St.
Louis, Mo., and a master’s degree in English from the University of Missouri, St. Louis.
KAYE FORGIONE, SENIOR ASSOCIATE, MATHEMATICS, ACHIEVE
Kaye Forgione joined Achieve as senior associate for mathematics in March 2001 where she
leads Achieve's Standards and Benchmarking Initiatives involving mathematics. Prior to joining
Achieve, Kaye served as assistant director of the Systemic Research Collaborative for
Mathematics, Science and Technology Education (SYRCE), a project at the University of Texas
at Austin funded by the National Science Foundation. Her responsibilities at the University of
Texas also included management and design responsibilities for UTeach, a collaborative project
of the College of Education and the College of Natural Sciences to train and support the next
generation of mathematics and science teachers in Texas. Before her work at the University of
Texas, Kaye was director of academic standards programs at the Council for Basic Education, a
nonprofit education organization located in Washington, DC. Prior to joining the Council for
Basic Education in 1997, Kaye worked in the K-12 arena in a variety of roles, including several
leadership positions with the Delaware Department of Education. Kaye began her education
career as a high school mathematics teacher. She taught mathematics at the secondary and
college levels as part of adult continuing education programs. Kaye received a bachelor’s degree
in mathematics and education from the University of Delaware, a master’s degree in systems
management from the University of Southern California, and a doctorate in educational
leadership from the University of Delaware.
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JAMES MACDONALD, PROJECT ASSOCIATE, ACHIEVE
James Macdonald supports Achieve’s Content & Policy Research work, editing and formatting
documents, as well as by providing content support. Before joining Achieve in 2004, James was
executive assistant and membership coordinator at the George C. Marshall Institute. At the same
time, he served as an adjunct philosophy professor at Catholic University of America and Mount
St. Mary’s College. James also has taught philosophy courses at the University of Toledo while
working on his graduate studies. He has had articles published in Philosophical Writings UK
and the Review of Metaphysics. James received a bachelor’s degree in philosophy and history
from Ohio Northern University and a master’s degree in philosophy from the University of
Toledo. He pursued a doctorate in philosophy from Catholic University of America, where he
has completed everything but his dissertation.
LAURA MCGIFFERT SLOVER, VICE PRESIDENT CONTENT & POLICY RESEARCH, ACHIEVE
Laura McGiffert Slover is Vice President of Content & Policy Research at Achieve, where she
has senior responsibility for overseeing a number of Achieve’s major initiatives. She supervises
Achieve’s Benchmarking Initiative, leads its work with states on building mathematics capacity,
and oversees the organization’s research agenda. Laura has extensive experience reviewing
academic standards and education policies in the United States and abroad, and she has written a
number of reports and articles on the topic. Before joining Achieve in 1998, Laura was a high
school English teacher in Eagle County, Colorado, where she was involved in the district's early
efforts to develop standards and benchmark assessments. She also taught writing and
composition at Colorado Mountain College. A native Washingtonian, Laura earned a bachelor’s
degree in English and American Literature from Harvard University; a master’s in Education
Curriculum and Instruction from the University of Colorado at Boulder; and a master's in
Education Policy from Georgetown University. She currently serves as a member of the Board
of Education of the District of Columbia.
DOUGLAS SOVDE, ASSOCIATE, MATHEMATICS, ACHIEVE
Douglas Sovde joined Achieve in 2008 as an associate for mathematics. His primary
responsibilities include leading reviews of state mathematics standards in support of Achieve’s
Alignment Institutes and the American Diploma Project. Prior to joining Achieve, Doug spent
12 years in the Bellevue (WA) Public Schools as a teacher, an assistant principal and a principal.
As a mathematics teacher, Doug taught courses from pre-algebra to AP Calculus BC. He later
became an assistant principal at Bellevue High School and Sammamish High School, where he
also supervised the mathematics departments. In 2006, Doug became the principal of Chinook
Middle School, where he managed the development of a new curriculum in mathematics,
science, and social studies. He also served as the liaison between the school district and the
University of Washington’s LIFE Center to provide staff development to principals and
curriculum developers on instructional leadership, curriculum development and classroom
instruction. Mr. Sovde earned a bachelor’s degree in mathematics from the University of
Washington, a master’s degree in Curriculum and Instruction from Western Washington
University, and his principal certification from the University of Washington’s Danforth
Educational Leadership and Policy Studies Program.
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CONTENT EXPERTS AND REVIEWERS IN ENGLISH LANGUAGE ARTS AND
MATHEMATICS
MELANIE ALKIRE
Melanie Alkire is currently a mathematics consultant with Achieve, Inc. and a site visitor and
higher level mathematics assistant examiner for International Baccalaureate North America.
Beginning in 1994, Ms. Alkire contributed to the design and implementation of the Oregon
University System’s framework of standards and assessments for admission to the seven public
university campuses called PASS (Proficiency-based Admissions Standards System). In this
project she served as Lead Teacher, Assessment Moderator and Site Coordinator, and was also
involved in the writing and implementation of proficiencies in mathematics, as well as project
evaluation and training and professional development of mathematics faculty and high school
teachers. She retired in 2005 from Portland Public Schools where she served as a mathematics
teacher, department chair, International Studies Coordinator, and International Baccalaureate
Coordinator. Ms. Alkire received an AB in Mathematics/Education from Northwest Nazarene
University and a MAT in Mathematics/Education from Lewis and Clark College.
JEROME HALPERN
Jerome Halpern is a consultant and a part time faculty member with Department of English at
the University of Pittsburgh, where he is the Coordinator for School Partnerships with the
Western Pennsylvania Writing Project. Mr. Halpern taught English for 30 years at Langley High
School in the Pittsburgh Public Schools and served as the English Department chairperson for 17
years. He also served as Director of the Health Careers Academy and as restructuring design
coach at the school (2 years). He served as director of the Applied Learning Teachers’ Institute
(5 years), a professional development program in the Pittsburgh Public Schools focusing on the
development of standards-driven performance-based units of instruction integrating content
standards and school-to-career instruction He worked in Pittsburgh on numerous English
language arts curriculum development teams, including the Arts Propel imaginative writing and
portfolio development team, a collaborative project of Educational Testing Service, Dr. Howard
Gardner’s Project Zero, and the Pittsburgh Public Schools. Mr. Halpern also chaired the
District’s Senior Graduation Project Development Committee. In addition, he worked with the
New Standards Project on the development of the English Language Arts Performance Standards
and the New Standards ELA and Applied Learning Portfolios and as a consultant with the
Learning Research and Development Center at the University of Pittsburgh. Mr. Halpern was a
member of the national faculty of the Modern Red Schoolhouse Institute from 1997 to 2003. He
is a National Writing Project Fellow; and, as a Fellow of the Carnegie Mellon University Center
for Community Outreach, he has worked with Dr. Linda Flower on workforce development
projects. He received a master’s degree in education from the University of Pittsburgh and a
bachelor’s degree in education from Duquesne University.
ELIZABETH HAYDEL
Elizabeth Haydel is an educational consultant whose current projects include work for Achieve,
the Ohio Department of Education’s Center for the Teaching Profession, and the Educational
Research Institute of America (ERIA). She was project manager for Indiana University's Center
for Innovation in Assessment, during which time she assisted in the development of the Indiana
standards and oversaw the creation of the Core 40 end-of-course, high-school assessments.
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January 15, 2009
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Subsequently, she served as an English Language Arts Consultant for the Ohio Department of
Education and a writer and editor for the American Institutes for Research (AIR). As consultant,
she has written reading workbooks, test passages and assessment items for various state
assessment and test preparation programs. A graduate of Stanford University with a degree in
American Studies, Ms. Haydel also holds a Masters degree in Language Education from Indiana
University.
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